Why does cosine sometimes change to sine?

Question

Mathematics

We study trigonometry at school, namely reduction formulas. It seems that everything is easy and understandable, but it is given as a fact: the sine is replaced by a cosine, the minus in front of the cosine is omitted, etc.
But why, for example, sin(pi/2+t)=cos(t)? Could you explain why this is so and not otherwise?

Answer 1

google =)

Answer 2

from Christmas to Easter four months
and from Easter to Christmas - eight

Answer 3

Cosine is cosine; sine shifted pi/2 to the right.